Day 1. Mental Arithmetic Questions KS3 MATHEMATICS. 60 X 2 = 120 seconds. 1 pm is 1300 hours So gives 3 hours. Half of 5 is 2.

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1 Mental Arithmetic Questions. The tally chart shows the number of questions a teacher asked in a lesson. How many questions did the teacher ask? 22 KS MATHEMATICS Level 4 Answers Day 2. How many seconds are there in two minutes? 0 X 2 = 20 seconds. What number is the arrow pointing to on the number line? 0 4. The time is now one p.m. My train is due at sixteen hundred hours. How many hours is it before my train is due? pm is 00 hours So gives hours. What is the next number in this halving sequence? Twenty, ten, five, Half of is 2.

2 Cards for fractions Here are six number cards (a) Choose two of these six cards to make a fraction that is equivalent to X2 2 Equations Solve these equations. a + 2 = 24 b 2 = = 2 2 a =... b =... 0 OR 2 4. Remember to multiply both the top and bottom numbers by the same number X = (b) Choose two of these six cards to make a fraction that is greater than 2 but less than 4 OR OR 8 0 OR 8 0 OR 8 0 OR 2 2 Café A café sells coffee and toast. Placing fractions cup of coffee cup of coffee Here are four fractions. slice of toast 2 slices of toast 4 8 Cost.0 Cost.70 Look at the number line below. Write each fraction in the correct box. How much does cup of coffee cost? 0 0. The only difference between the two is second one has an extra piece of toast. So the toast must cost = 40p marks So the coffee must cost.0 40p, which gives 90p p

3 Mental Arithmetic Questions KS MATHEMATICS Level 4 Answers Day 2. A teacher asked some pupils if they had a part-time job. The pie chart shows the results. The teacher asked twenty pupils. How many of them said yes? Yes is a quarter of the pie, so the teacher asked a quarter of =, so students 2. Four packets of biscuits cost one pound. How much would six packets of biscuits cost? 4 = 2p, so each biscuits costs 2p. X 2 p = 0p or.0.. Look at the rectangle. What is its perimeter? 7 cm Perimeter is the distance around a shape, so 8cm + 7cm + 8cm + 7cm. This gives 0 cm. Remember to put the lengths of the missing sides! 8 cm 4. Look at the expression in the square. Which answer below is the same as the expression in the square? Ring the correct on.. Look at the equation. When x equals five, what is the value of y? y = X + y = + y = 2

4 Weighing a dog Jack weighs himself kg Hexagons I use two congruent trapeziums to make the shapes below. Tick ( ) all the shapes that are hexagons. Hexagons have sides! Then Jack weighs himself together with his dog. 2 marks and 0.4 kg Four cubes I join three cubes in a line to make this shape. How much does the dog weigh? =.. Decimals This pair of decimal numbers add to (a) Write a different pair of decimal numbers that add to Lots of different answers: 0.2 and 0.8 OR 0. and 0.9 OR 0.4 and 0. OR 0. and 0. Can by any order. Then I join one more cube to make an L-shape. Draw the L-shape on the paper below. (b) The pair of decimal numbers below should add to Write the missing decimal number marks

5 Mental Arithmetic Questions. The diagram shows a line inside a square. What is the size of the angle labelled t? KS MATHEMATICS Level 4 Answers Day Angles inside a square are 90 o, so 90 0 = 0 0 o 2. In my family, the range of heights is 2 cm. The height of the shortest person is 2 cm. What is the height of the tallest person? Range means the difference between the largest and the smallest, so something take away 2 cm gives 2 cm = 0, so 0 cm.. Multiply 4.7 by X 00 gives 400, so 4.7 X 00 = Look at the triangle. Work out the size of angle a. The sum of the angles in a triangle is 80 o, so first add the two angles. o + 70 o = 0 o. Then 80 o 0 o = 7 o. What is the next prime number after nineteen? Remember: Prime numbers have exactly 2 factors ( and the number itself). Answer: 2

6 Caribbean cordial Here are the ingredients for a cordial used to make a drink. (a) OR 4 (b) 0g ginger lemon. litres of water 900g sugar Jenny is going to make this cordial with 2g of ginger. How much lemon, water and sugar should she use? 2g ginger... 2 lemon litres of water...g 40 sugar The finished drink should be cordial and 2 water. Jenny puts 00 ml of cordial in a glass. How much water should she put with it? 2 is half of 0 (which is the amount in the original recipe), so half the amounts of everything! marks Throwing dice Some pupils throw two fair six-sided dice. Each dice is numbered to. One dice is blue. The other dice is red. Anna s dice show blue, red. Her total score is 8. The cross on the grid shows her throw. (a) (b) (c) Carl s total score is. What numbers could Carl s dice show? Put crosses on the gird to show all the different pairs of numbers Carl s dice could show. The pupils play a game. Winning rule: Win a point if the number on the blue dice is the same as the number on the red dice. 2 marks Put crosses on the grid to show all the different winning throws. The pupils play a different game. The grid shows all the different winning throws. 4 red 2 4 red 2 4 red 4 red 2 2 X 2 4 blue 2 4 blue 2 4 blue 2 4 blue X X X X X X X X X 2 marks If one third is 00 ml, then two thirds must be twice this! ml Complete the sentence below to show the winning rule. Winning rule: Win a point if the number on the blue dice is One more than the number on the red dice...

7 Mental Arithmetic Questions. What is 20% of 00? To find 0%, divide by 0, so 0% is 00 0, which is 0. 20% is double this, so 0 X 2 gives It takes hours to travel from my home to my friend s house. I arrive at 2:00 pm. At what time did I leave home? Write your answer using am or pm. hours before 2:00 pm is :00 am. I count back in nought point ones. Write the next two numbers in the pattern below ,.2,.,, 4. Subtract 9 pence from 0. 9 pence is 0.09, so gives 9.9. Shade one quarter of the diagram below. There are 8 little squares, and a quarter of 8 gives 2. So shade any 2 little

8 Write a number (a) Write a number that is both greater than 0 and a multiple of 4 2 or or 20 or... (b) Now write a number that is both greater than 0 and a square number Spinners On each spinner write five numbers to make the statements correct. It is certain that you will get a number less than 2 4 This is one example. Put any numbers in each triangle, but the numbers must be less than. A square number is a number multiplied by itself. squared ( 2 ) is X = 9. Shampoo The diagram shows what Molly buys., 2,, 49,... It is more likely that you will get an even number than an odd number. You must have at least even numbers It is impossible that you will get a multiple of She pays with a note and gets p change. Put any numbers, but do not use multiples of (i.e.,, 9, 2,, ) How much did Molly pay for the shampoo? p gives 4.4. The hand cream and soap give p = gives.. 2 marks

9 . Add 72 and 8. Mental Arithmetic Questions KS MATHEMATICS Level 4 Answers Day Try to give 00, then to give 0. Then to give Centimetres are a measure of length. What are Grams a measure of? Mass. How much is half of 9.0? The diagram shows a plan of a room. The scale is centimetres to 2 metres. On the plan the room is 4 cm long. How long is the room in real life? 4 X 2 = 8 8 metres. The pie chart shows how two hundred pupils travel to school. How many of these pupils walk to school? Walking is a quarter of the pie, so a quarter of 200 gives 0 students

10 Populations The table shows the approximate populations of five different places. Place Approximate population London Sheffield Harrogate Ash Vale Binbrook 700 Thinking of rules (a) I can think of three different rules to change to 8 8 Complete these sentences to show what these rules could be. (a) Which of the places has a population of about seventy thousand?... Harrogate (b) Use the table to complete these sentences. The population of Harrogate is about 0 times as big as first rule: second rule: 2 add... multiply by... the population of... London Ash Vale The population of... is about 00 times as big as third rule: multiply by 2 then... the population of Harrogate. The population of Sheffield is about... times as big as the population of Ash Vale. Number lines 00 2 marks (b) Now I think of a new rule. The new rule changes 0 to and it changes 8 to Write the missing numbers on the number lines Write what the new rule could be. Divide by marks

11 Mental Arithmetic Questions. The population of the United Kingdom is about fifty-nine million. Write this number in figures KS MATHEMATICS A pupil measures his height as six feet. About how many metres is that? Ring the best answer below Level 4 Answers Day. Write a multiple of that is bigger than or 0 or 08 or or 4. Look at the angle. Estimate its size in degrees. Actual is o Accept 2 o - 4 o. Look at the expression. Write it as simply as possible. a + 4a + 2a 9a

12 Which calculation? Here is some information about a school. There are classes in year 8. Each class has 27 pupils. There are 4 classes in year 9. Each class has 2 pupils. (b) Use the information about the school to write what the missing question could be. Question Calculation (a) Use the information to match each question with the correct calculation. The first one is done for you. Question Calculation How many students are there in Year 9? How many classes are there altogether in years 8 and 9? 4 Chains (a) The number chain below is part of a doubling number chain. 4 Fill in the two missing numbers. There are more classes in year 9 than in year 8. How many more? How many pupils are there altogether in years 8 and 9? ( 27) + (4 2) ( + 27) + (4 + 2) ( 27) (4 2) (b) The number chain below is part of a halving number chain. Fill in the two missing numbers. There are more pupils in year 9 than in year 8. How many more? (4 + 2) ( + 27) (4 2) ( 27) marks

13 Mental Arithmetic Questions. In a local swimming pool, 2 lengths is half a mile. How many lengths is one mile? 2 X 2 = 4 lengths KS MATHEMATICS Level 4 Answers Day 7 2. I bought three tickets for a concert. The total cost was 4. How much was one ticket? 4 =. Below is part of a train timetable. How long does the journey take from Twyford to Maidenhead? minutes 4. What is one quarter of 0? 0 4 =. What is the perimeter of this square? 0 X 4 = 40 cm 0 cm

14 Place value Shapes on a grid (a) Add together 740 and 282 Here is a sequence of shapes made with grey and white tiles. Shape number Shape number 2 Shape number Shape number (b) Now add together 7.4 and 2.82 You can use part (a) to help you (c) is bigger than How much bigger? The number of grey tiles = 2 the shape number The number of white tiles = 2 the shape number (a) Altogether, how many tiles will be in shape number? = = = X = tiles 0.4 (b) Altogether, how many tiles will be in shape number? 2 marks 4 X = tiles (c) Write the missing number below. 4 The total number of tiles =... the shape number

15 Mental Arithmetic Questions. Look at the numbers. Put a ring round the median. The median is the middle number when all the numbers are in order Look at the scale. About what value is the arrow pointing to?.8 KS MATHEMATICS Level 4 Answers Day 8 8. My birthday is 22 days after my friend s birthday. This year my friend s birthday is on a Monday. On what day will my birthday be this year? Monday will be every 7 days, so after weeks ( X 7 = 2 days) it will be Monday. This means the 22 nd day will be a Tuesday. 9. The longest flight of stairs in the world is in Switzerland. There are 74 steps. Write this number to the nearest thousand What is the largest number that will divide exactly into 2 and 20? 2 X = 0 20 X = 0 So 0

16 Computation (a) Add together.7 and. Completing quadrilaterals (a) The line on the square grid below is one side of a square. Draw more lines to complete the square (b) Subtract.7 from (c) Multiply 24 by Quick Method: Multiply by 0 then half your answer! (d) Divide 42 by Quick Method: Multiply by 2, then multiply by! (b) The line on the square grid below is one side of a quadrilateral. The quadrilateral has only one pair of parallel sides. Draw more lines to show what the quadrilateral could be. You need to draw a trapezium. Two possibilities are shown.

17 Mental Arithmetic Questions. I buy a notebook for 0p. How much change should I get from a 2 coin? 2 0p =.0 KS MATHEMATICS Add these numbers: Level 4 Answers Day 9. A train leaves at 0:0 am and travels for 4 hours. At what time does the train stop? Write your answer using am or pm. 2:0 pm 4. I am counting back in steps of 0. Write down the next number. 2,, 0, 9. What is half of seven?.

18 Signs Use +,, or to make each calculation correct. Examples: = = = = = Survey results (a) 2 for Yes plus for No makes = 9 Jackie asked 27 people: Do you like school dinners? The bar chart shows her results for Yes and No. Complete the bar chart to show her result for Don t know. Number of people = (b) 2 0 Yes No Don t know This pictogram also shows her results for Yes and No. Complete the pictogram to show her result for Don t know. Yes No has two circles for a total of. This means each circle is worth people. So for 9 people we need circles No Don t know

19 Mental Arithmetic Questions. Look at the temperatures below. Put a ring round the temperature that is the lowest. KS MATHEMATICS Level 4 Answers Day people went on holiday. The pie chart shows how they travelled. How many people travelled by car? A quarter of the pie is Car, so a quarter of 00 gives 0 people. Write down an even number that is a multiple of seven. 4 or 28 or 42, etc. 4. Two rulers cost 80p. How much do rulers cost? One ruler costs 80 2 = 40p. So X 40p gives 20 or.20. How many seconds are there in one and a half minutes? 0 seconds in one minute, so 0 seconds in half a minute, this gives 90 seconds in one and a half minutes.

20 Temperature The arrow by this thermometer shows a temperature of 20 C ºC 0 (a) Draw an arrow by the thermometer to show 7 C. Label your arrow 7 C 20 20ºC Names These are the names of the twelve people who work for a company. Ali Claire Kiki Suki Brian Claire Lucy Tom Claire James Ryan Tom (a) What name is the mode? Mode means the most! Claire o C - o C (b) Draw an arrow by the thermometer to show C. Label your arrow C (c) In New York the temperature was 2 C In Atlanta the temperature was 7 C warmer. What was the temperature in Atlanta?... C (d) In Amsterdam the temperature was C In Helsinki the temperature was 8 C How many degrees warmer was it in Amsterdam than in Helsinki? (b) Television One person leaves the company. A different person joins the company. Now the name that is the mode is Tom. Write the missing names in the sentences below. The name of the person who leaves is... The name of the person who joins is... I buy a widescreen television costing 290 I pay 900 now, then I pay the rest of the money in equal payments. How much is each payment? Show your working = 90 Claire Tom... C 90 = marks